This invention relates to an air-fuel ratio sensor for detecting an air-fuel ratio of an air-fuel mixture to be supplied to a variety of combustion equipment such as an internal combustion engine or the like on the basis of oxygen concentration in an exhaust gas.
Conventionally, an air-fuel ratio sensor of the kind as described above, uses a detection element in which a pair of porous electrodes are respectively laminated on opposite surfaces of a solid electrolyte having oxygen-ion conductivity.
Such an air-fuel ratio sensor is called a diffusion limited current type as disclosed, for example in Japanese Patent Unexamined Publication No. 57-48648/1982, Japanese Utility Model Unexamined Publication No. 60-17452/1985. In the diffusion limited current type gas sensor a porous gas-diffusion limiting layer, for limiting diffusion of a measuring gas is formed on one of the porous electrode surfaces of the foregoing detection element either directly or through a closed space. The electrode at the gas-diffusion limiting layer side is used as a cathode, and a predetermined voltage is applied between the electrodes so as to detect an air-fuel ratio on the basis of a diffusion limited current flowing at this time. Further, there has been an air-fuel ratio sensor as disclosed, for example, in Japanese Patent Unexamined Publication No. 59-178354/1984, in which two detection elements, each arranged in the same manner as described above, are disposed so as to cause the respective porous electrodes thereof to contact with a measuring gas chamber in which diffusion of a measuring gas is limited by a gas-diffusion limiting layer. One of the detection elements acts as an oxygen pumping element while the other detection element acts as an oxygen concentration cell element so that an air-fuel ratio is detected on the basis of a current flowing in the oxygen pumping element or a voltage generated between the electrodes at the opposite ends of the oxygen concentration cell element.
In the foregoing detection elements, however, the current flowing when a predetermined voltage is applied between the porous electrodes when a predetermined current is flowed through the porous electrodes, or the voltage generated between the porous electrodes, may vary depending on the temperature when the detection elements are in use. Therefore, there has been a problem in that in order to obtain a stable detection signal by using the foregoing air-fuel ratio sensor, it is necessary to maintain the detection elements at a predetermined temperature.
Various efforts have been made to solve the problem of the temperature dependence of the detection signal of the air-fuel ratio sensor of the kind described above to thereby enlarge the range of the temperatures at which the air-fuel ratio sensor can be used. For example, as disclosed in Japanese Patent Unexamined Publication No. 59-67454/1984, the pore size of the gas-diffusion limiting layer formed on the detection element on one of the porous electrodes was set to 300 .ANG.-400 .ANG..
When the thus arranged air-fuel ratio sensor was attached to actual combustion equipment (for example, an internal combustion engine) and operated, the detection signal varied as the pressure in the exhaust system fluctuated so that no stable detection signal could be obtained, even though the exhaust gas temperature remained stable. That is, in combustion equipment, not only the exhaust gas temperature, but also the exhaust gas pressure, vary depending on the running state of the combustion equipment. Therefore, no stable detection signal can be obtained even if the problem of the temperature dependence of the detection signal could be solved as described above.
When the gas-diffusion limiting layer having a pore size of 300 .ANG.-400 .ANG. is used as described above, a rate of molecular diffusion is reduced when a measuring gas passes through the gas-diffusion limiting layer. That is, when the gas-diffusion limiting layer is formed on one of the porous electrodes and a predetermined voltage is applied between the electrodes, with the one electrode as a cathode, a current I flowing in the detection element can be represented by the following expression (1): EQU I.alpha.4.multidot.F.multidot.S.multidot.Dg.multidot.Pg/R.multidot.T.multid ot.L (1)
where F represents Faraday constant, R a gas constant, S a sectional area of the diffusion pore of the gas-diffusion limiting layer, T an absolute temperature, L a thickness of the gas-diffusion limiting layer, Pg the partial pressure of oxygen gas in the measuring gas, and Dg a diffusion coefficient of the measuring gas.
Further, diffusion of the measuring gas is divided into molecular diffusion represented by a diffusion coefficient Dm shown by the following expression (2), and fine pore diffusion (Knudsen diffusion) represented by a diffusion coefficient Dk shown by the following expression (3): EQU Dm.alpha.T.sup.1.75 .multidot.Pa.sup.-1 ( 2)
where Pa represents the total pressure of the measuring gas atmosphere; and EQU Dk.alpha.r.multidot.T.sup.0.5 .multidot.M.sup.-0.5 ( 3)
where r represents the mean pore size and M the molecular weight of the measuring gas.
When the measuring gas passes through the gas-diffusion limiting layer only by molecular diffusion, the current I flowing in the detection element is represented by the following expression (4): EQU I.alpha.T.sup.0.75 .multidot.S/L (4)
where Pg.alpha.Pa.
When the measuring gas passes through the gas-diffusion limiting layer only by fine pore diffusion, the current I flowing in the detection element is represented by the following expression (5): EQU I.alpha.T.sup.-0.5 .multidot.Pg.multidot.S/L (5)
Accordingly, the current I actually flowing in the detection element can be represented by the following composite expression (6) of the foregoing expression (4) and (5): EQU I.alpha.(K1.multidot.T.sup.0.75 .multidot.S/L+K2.multidot.T.sup.-0.5 .multidot.Pg.multidot.S/L) (6)
where K1 and K2 represent coefficients and K1+K2=1.
Therefore when the air-fuel ratio sensor is formed by using the gas-diffusion limiting layer having a pore size of 300 .ANG.-400 .ANG., the rate of the fine pore diffusion represented by the foregoing expression (5) becomes large, so that the detection signal is influenced by the oxygen partial pressure Pg in the measuring gas which varies in proportion to the measuring gas atmosphere total pressure (exhaust gas system pressure) Pa.
Further, in order to solve the problem of pressure dependence of the detection signal, the pore size of the gas-diffusion limiting layer may be made large to thereby increase the rate of the molecular diffusion represented by the foregoing expression (4). If merely the pore size of the gas-diffusion limiting layer is made large, however, there have been such problems that not only the temperature dependence of the detection signal becomes large but also deposits such as Pb, P, S, and the like, which are contained in an exhaust gas and which are harmful to an electrode material, are transmitted through the gas-diffusion limiting layer.